the mechanism of [1]} gives
a \(\displaystyle r_p:W_F\rightarrow S\hat{}\)  such that
\(t(\sigma ,\sigma ^{\prime })=r_p(\sigma )^{\sigma ^{\prime }}r_p(\sigma \sigma ^{\prime })^{-1}r_p(\sigma ^{\prime })\;\;\text{\rm for all $\displaystyle \sigma , \sigma ^{\prime }\in W_F$}\) 
